What is log_{10}((x^2y^3)/(100)) ?

The solution to log_{10}((x^2y^3)/(100)) is 2log_{10}(x)+3log_{10}(y)-2

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simplify log_{10}((x^2y^3)/(100))

simplify

lo g_{10} (\frac{x ^{2} y ^{3}}{100})

2 lo g_{10} (x) + 3 lo g_{10} (y) - 2

Solution steps

lo g_{10} (\frac{x ^{2} y ^{3}}{100})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{10} (\frac{x ^{2} y ^{3}}{100}) = lo g_{10} (x^{2} y^{3}) - lo g_{10} (100)

= lo g_{10} (x^{2} y^{3}) - lo g_{10} (100)

lo g_{10} (x^{2} y^{3}) = 2 lo g_{10} (x) + 3 lo g_{10} (y)

lo g_{10} (100) = 2

= 2 lo g_{10} (x) + 3 lo g_{10} (y) - 2

- \frac{4}{7} \cdot lo g_{2} (\frac{4}{7}) - \frac{3}{7} \cdot lo g_{2} (\frac{3}{7})

lo g_{5} (\frac{( \frac{5 x}{x + 2} )}{x + 6} \cdot x)

- lo g_{10} (7.1 \cdot 1 0^{- 4})

ln (\frac{1}{- 1})

lo g_{3} (x) + lo g_{3} (x - 2)

What is log_{10}((x^2y^3)/(100)) ?
The solution to log_{10}((x^2y^3)/(100)) is 2log_{10}(x)+3log_{10}(y)-2